Example 2 - Chapter 13 Class 12 Probability

Last updated at April 16, 2024 by

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Example 2 A family has two children. What is the probability that both the children are boys given that at least one of them is a boy ? A Family has two children Let girls be denoted by ‘g’ & boys be denoted by ‘b’ S = {(g, g), (g, b), (b, g), (b, b)} We need to find the probability that both the children are boys, given at least one them is a boys E: Both the children are boys F: At least one of the children is a boys We need to find P(E|F) E : both the children are boys E = {(b, b)} P(E) = 𝟏/𝟒 F : at least one of the children is a boy F = {(g, b), (b, g), (b, b)} P(F) = 𝟑/𝟒 Also, E ∩ F = {(b, b)} P(E ∩ F ) = 𝟏/𝟒 Now, P(E|F) = (𝑃(𝐸 ∩ 𝐹))/(𝑃(𝐹)) = (1/4)/(3/4) = 𝟏/𝟑

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.